SOLUTION: The given value of a fraction is 3/8. If 7 is added to the numerator & subtracted from the denominator, the value of the resulting fraction becomes 2/3.What is the original form o

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Question 984760: The given value of a fraction is 3/8. If 7 is added to the numerator & subtracted from the denominator, the value of the resulting fraction becomes 2/3.What is the original form of the fraction?
Found 2 solutions by Fombitz, vleith:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Start with 3%2F8 and multiply numerator and denominator by some non-zero integer, n.
Then add and subtract 7 as noted.
%283n%2B7%29%2F%288n-7%29=2%2F3
3%283n%2B7%29=2%288n-7%29
9n%2B21=16n-14
7n=35
n=5
So then,
%283%2A5%29%2F%288%2A5%29=highlight%2815%2F40%29

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You are told the original fraction is equal to 3%2F8
Let X be nonzero
3%2F8+=+%283x%29%2F%288x%29
You are then told that if 7 is added to the numerator & subtracted from the denominator, the value of the resulting fraction becomes 2/3.
So %283x%2B7%29%2F%288x-7%29+=+2%2F3
9x+%2B+21+=+16x+-14
35+=+7x
5+=+x
So the original fraction was 15%2F40